Magicians use an Elemental Grimoire as the book/container for their research.
The Magician advanced research book Arch Magus Grimoire may also be used.

Magicians use the results of spell research as components for furthering their research.
ie. a level 16 spell scroll is used in creating a level 20 spell scroll, etc.

To abbreviate spell names below I will refer to each element by a single letter:
[A] for Air, [E] for Earth, [F] for Fire and [W] for Water.
For simplicity I will refer to spells with the title Flame as Fire and Mist as Air.

Casters Realm also provides information for Concordance of Research which is summarized here.
( Research listings for the Enchanter, Necromancer and Wizard classes. )
( Advanced research listings for the Enchanter, Necromancer, Wizard or all classes. )

SPELL RESEARCH DETAILS
Lev	Spell	Components Required
16	Minor Summoning [A]	Level 12 Spell Elemental [A]	Words of Tyranny	Aviak Feather
16	Minor Summoning [E]	Level 12 Spell Elemental [E]	Words of Tyranny	Small Brick of Ore
16	Minor Summoning [F]	Level 12 Spell Elemental [F]	Words of Tyranny	Halas Heater
16	Minor Summoning [W]	Level 12 Spell Elemental [W]	Words of Tyranny	Shark Skin
20	Lesser Summoning [A]	Minor Summoning [A]	Words of Dominion	Pearl Shard
20	Lesser Summoning [E]	Minor Summoning [E]	Words of Dominion	Topaz
20	Lesser Summoning [F]	Minor Summoning [F]	Words of Dominion	Jade Shard
20	Lesser Summoning [W]	Minor Summoning [W]	Words of Dominion	Ice of Velious
24	Cornucopia	Summon Food	Words of Transcendence	Loaf of Bread
24	Everfount	Summon Drink	Words of Transcendence	Water Flask
24	Summoning [A]	Lesser Summoning [A]	Words of Dimension	Pearl Shard
24	Summoning [E]	Lesser Summoning [E]	Words of Dimension	Gloves of Rallos Zek
24	Summoning [F]	Lesser Summoning [F]	Words of Dimension	Jade Shard
24	Summoning [W]	Lesser Summoning [W]	Words of Dimension	Ice of Velious
29	Greater Summoning [A]	Summoning [A]	Words of Coercion	Scent of Marr
29	Greater Summoning [E]	Summoning [E]	Words of Coercion	Gloves of Rallos Zek
29	Greater Summoning [F]	Summoning [F]	Words of Coercion	Breath of Solusek
29	Greater Summoning [W]	Summoning [W]	Words of Coercion	Flame of Vox
29	Summon Coldstone	Summon Heatstone	Words of Sight	Eye of Serilis
34	Minor Conjuration [A]	Greater Summoning [A]	Words of Duress	Scent of Marr
34	Minor Conjuration [F]	Greater Summoning [F]	Words of Duress	Breath of Solusek
34	Nullify Magic	Cancel Magic	Words of Detention	Blood of Velious
39	Lesser Conjuration [E]		Words of Convocation	Gloves of Rallos Zek
39	Lesser Conjuration [W]		Words of Convocation	Flame of Vox
39	Summon Mystic Dagger		Words of Collection (Azia)	Dagger
39	Summon Ring of Flight		Words of Collection	Star Rose Quartz
44	Conjuration [A]	Lesser Conjuration [A]	Words of Incarceration	Scent of Marr
44	Conjuration [E]	Lesser Conjuration [E]	Words of Incarceration	Essence of Rathe
44	Conjuration [F]	Lesser Conjuration [F]	Words of Incarceration	Breath of Ro
44	Conjuration [W]	Lesser Conjuration [W]	Words of Incarceration	Tears of Prexus
49	Greater Conjuration [A]	Conjuration [A]	Words of Bondage	Wings of Xegony
49	Greater Conjuration [F]	Conjuration [F]	Words of Bondage	Breath of Ro
49	Greater Conjuration [W]	Conjuration [W]	Words of Bondage	Tears of Prexus

SPELL RESEARCH CATALOG
Component	Lev	Spell [Air, Earth, Fire, Water]
Words of Bondage	49	Greater Conjuration [A,F,W]
Words of Coercion	29	Greater Summoning [A,F,W]
Words of Collection	39	Summon Ring of Flight
Words of Collection (Azia)	39	Summon Mystic Dagger
Words of Convocation	39	Lesser Conjuration [E,W]
Words of Detention	34	Nullify Magic
Words of Dimension	24	Summoning [A,E,F,W]
Words of Dominion	20	Lesser Summoning [A,E,F,W]
Words of Duress	34	Minor Conjuration [A,F]
Words of Incarceration	44	Conjuration [A,E,F,W]
Words of Sight	29	Summon Coldstone
Words of Transcendence	24	Cornucopia
		Everfount
Words of Tyranny	16	Minor Summoning [A,E,F,W]
Aviak Feather	16	Minor Summoning [A]
Blood of Velious   ($)	34	Nullify Magic
Breath of Ro	44	Conjuration [F]
	49	Greater Conjuration [F]
Breath of Solusek   ($)	29	Greater Summoning [F]
	34	Minor Conjuration [F]
Dagger   ($)	39	Summon Mystic Dagger
Essence of Rathe	44	Conjuration [E]
Eye of Serilis	29	Summon Coldstone
Flame of Vox	29	Greater Summoning [W]
	39	Lesser Conjuration [W]
Gloves of Rallos Zek	24	Summoning [E]
	29	Greater Summoning [E]
	39	Lesser Conjuration [E]
Halas Heater   ($)	16	Minor Summoning [F]
Ice of Velious	20	Lesser Summoning [W]
	24	Summoning [W]
Jade Shard	20	Lesser Summoning [F]
	24	Summoning [F]
Loaf of Bread   ($)	24	Cornucopia
Pearl Shard	20	Lesser Summoning [A]
	24	Summoning [A]
Scent of Marr   ($)	29	Greater Summoning [A]
	34	Minor Conjuration [A]
	44	Conjuration [A]
Scroll of the Element	16	Summon Heatstone
Shark Skin	16	Minor Summoning [W]
Small Brick of Ore   ($)	16	Minor Summoning [E]
Star Rose Quartz   ($)	39	Summon Ring of Flight
Tears of Prexus	44	Conjuration [W]
	49	Greater Conjuration [W]
Topaz   ($)	20	Lesser Summoning [E]
Water Flask   ($)	24	Everfount
Wings of Xegony	49	Greater Conjuration [A]
Spell: Cancel Magic   ($)	34	Nullify Magic
Spell: Summon Drink   ($)	24	Everfount
Spell: Summon Food   ($)	24	Cornucopia
Spell: Summon Heatstone   ($)	29	Spell: Summon Coldstone